| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Zero-sum game stable solution |
| Difficulty | Moderate -0.8 This is a standard game theory question requiring routine application of minimax/maximin algorithms to find play-safe strategies and saddle points. The procedures are algorithmic with no conceptual difficulty—students simply find row minima, column maxima, and check for equality. While it requires careful arithmetic across multiple steps, it involves no problem-solving insight or novel reasoning, making it easier than average. |
| Spec | 7.08c Pure strategies: play-safe strategies and stable solutions7.08d Nash equilibrium: identification and interpretation |
| I | II | III | IV | |
| I | \(-4\) | \(-5\) | \(-2\) | 4 |
| II | \(-1\) | 1 | \(-1\) | 2 |
| III | 0 | 5 | \(-2\) | \(-4\) |
| IV | \(-1\) | 3 | \(-1\) | 1 |
A two-person zero-sum game is represented by the following pay-off matrix for player $A$.
\begin{tabular}{c|cccc}
& I & II & III & IV \\
\hline
I & $-4$ & $-5$ & $-2$ & 4 \\
II & $-1$ & 1 & $-1$ & 2 \\
III & 0 & 5 & $-2$ & $-4$ \\
IV & $-1$ & 3 & $-1$ & 1
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Determine the play-safe strategy for each player. [4]
\item Verify that there is a stable solution and determine the saddle points. [3]
\item State the value of the game to $B$. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q2 [8]}}